Solve Before You Teach¶

Strategy · All strategies
Evidence · no claims cited

Description¶

Solve Before You Teach is a preparation strategy in which the instructor completes the target task — problem, reading, design challenge, or proof — before planning instruction. The instructor attends to their own solution process: where they hesitated, which approaches they tried and rejected, and where errors are likely. These observations become the basis for anticipating learner difficulties, selecting which student approaches to highlight, and planning questions and Scaffolding moves.

Design Implications¶

Solving the task first converts the instructor's tacit expertise into usable pedagogical knowledge. Expert performance is often automated and inaccessible to introspection; deliberately re-solving a task slows it down and makes decision points visible again, which is the same mechanism that makes Think-Aloud modeling effective for learners. The strategy is central to "anticipating" in the five practices model of orchestrating discussion, where teachers work the task and predict the strategies students will produce [Stein et al. (2008) [+M]. It also underpins pedagogical content knowledge: knowing not just the content but the typical errors and productive representations associated with it [Ball, Thames, & Phelps, 2008] [+M].

Context¶

Requirements¶

• Genuine engagement with the task, not just reading an answer key — the value lies in the solution process, not the final answer
• Deliberate attention to alternative solution paths, since learners will not follow the instructor's route
• Time in planning to record anticipated difficulties, misconceptions, and questions before instruction
• Willingness to notice one's own expert blind spots, where steps feel obvious but are not

Constraints¶

• Experts systematically underestimate task difficulty after automatization; solving once may not be enough — solving as a novice would (with fewer resources, no shortcuts) is more diagnostic [~M]
• Anticipations anchored to the instructor's own single solution path narrow the discussion and miss legitimate alternative strategies [-M]
• For open-ended or ill-structured tasks, a single personal solution provides weak anticipation; multiple solution attempts or Case Studies of prior learner work are needed [~M]
• Time-intensive; scales poorly across many distinct tasks unless tasks are reused or anticipated difficulties are documented and shared across instructors

Implementation Variability¶

• Solve as a novice: deliberately restrict yourself to the resources and prior knowledge learners will have
• Solve multiple ways: generate two or three solution paths to broaden anticipation
• Solve with errors: intentionally make plausible errors to map the misconception space
• Collaborative solving: a teaching team solves the task together and pools anticipations (common in lesson study and Cognitively Guided Instruction)
• Solve then compare with student work: after teaching, compare anticipations against actual learner responses to calibrate future planning

Target Learners¶

• All learners benefit indirectly, but the payoff is largest for novices, whose difficulties are least predictable from intuition alone and most dependent on the instructor having mapped the misconception space [+M]
• Especially valuable in discussion-based settings where the instructor must recognize and sequence unfamiliar student strategies in real time [+M]

Target Learning Goals¶

• Conceptual understanding: anticipating misconceptions enables instruction that confronts rather than avoids them
• Problem-solving and procedural fluency: selecting and sequencing multiple solution strategies for comparison
• Discussion facilitation: preparing to connect student ideas to disciplinary norms

Instructions¶

1. Obtain the task exactly as learners will see it — no answer key, no instructor notes.
2. Solve it, narrating or noting your own decision points, hesitations, and dead ends (a private Think-Aloud).
3. Solve it at least one additional way, ideally the way a novice might attempt it.
4. List anticipated learner strategies, common errors, and the questions that would move a stuck learner forward without giving away the path.
5. Plan which strategies to sequence during discussion and how to connect them to the target concept (Stein et al., 2008) [+M].
6. After instruction, compare anticipations with actual learner work and revise.

Related Strategies¶

• Anticipating Student Responses — the five-practices step this strategy feeds directly
• Lesson Study — institutionalizes collaborative task-solving before teaching
• Error Analysis — extends anticipation into a systematic map of misconceptions
• Teach AI through holistic, active, collaborative pedagogical strategies starting from real problem solving

Examples¶

• Five Practices for Orchestrating Productive Mathematics Discussions (Smith & Stein, 2011) — "anticipating" is the first practice: teachers solve the task, generate likely student strategies, and plan monitoring questions before the lesson.
• Cognitively Guided Instruction (CGI) — teachers solve word problems and map the strategy continuum children typically use, so instruction starts from anticipated student thinking rather than the textbook procedure.
• Productive Failure lessons (Kapur) — the instructor designs the task having already mapped canonical and non-canonical solution paths, so that learner-generated (often failed) attempts can be consolidated into the expert solution (Kapur, 2012) [+S].

Key Sources¶

• Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340. doi:10.1080/10986060802229675
• Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. doi:10.1177/0022487108324554
• Kapur, M. (2012). Productive failure in learning the concept of variance. Instructional Science, 40(4), 651–672. doi:10.1007/s11251-012-9209-6
• Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. doi:10.5951/jresematheduc.26.2.0114
• Smith, M. S., & Stein, M. K. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. NCTM.